TR30.1AH/97/4/004
Telecommunications Industry Association (TIA)
TR30.1 Ad-Hoc Group Meeting on PCM Modems
Norcross, GA, April 1997
COMMITTEE CONTRIBUTION
Technical Committee TR-30 Meetings
SOURCE:
Analog Devices, Inc.
CONTACT:
Joshua Kablotsky
phone:
(617) 461-3586
fax:
(617) 461-4241
email:
joshua.kablotsky@analog.com
TITLE:
Evaluation of DC suppression techniques
PROJECT:
PN-3838
DISTRIBUTION:
Members of TR-30.1 and meeting attendees
ABSTRACT
Other contributions have proposed various techniques for transmit spectral shaping, specifically DC suppression.
This contribution offers a method for consistent evaluation of spectral shaping techniques, analyzes the performance
of several proposed techniques, and makes specific recommendations to adopt a frame-based inversion algorithm
with a variable frame size.
Copyright Statement
The contributor grants a free, irrevocable license to the Telecommunications Industry Association (TIA) to
incorporate text contained in this contribution and any modifications thereof in the creation of a TIA standards
publication; to copyright in TIA’s name any standards publication even though it may include portions of this
contribution; and at TIA’s sole discretion to permit others to reproduce in whole or in part the resulting TIA
standards publication.
1. Introduction
Several contributions have described the need to remove spectral components at DC and low frequencies. Other
contributions have proposed methods for removing these spectral components. A uniform method is proposed for
analyzing the performance of these techniques.
Some contributions have highlighted the need for variable redundancy spectral shaping. Some contributions have
simulated performance of an algorithm across different frame sizes. This contribution studies the performance of
different algorithms across a wider range of frame sizes, at varying levels of redundancy, using different
constellation sizes.
This contribution asserts that an interleaved frame inversion technique using a large frame size with variable
redundancy offers the best compromise between low-frequency suppression, redundancy, and variable coding.
2. Measuring DC Suppression
Most committee members agree with the need to suppress the transmit spectrum at and around DC for the following
reasons. First, non-linear distortion is believed to be greater at low frequencies. Secondly, there is believed to be a
null in the channel at and around DC; recovery of the signal near this null would produce unacceptable noise
enhancement. Thirdly, noise from AC powerlines at 50/60Hz and associated low-order harmonics presents SNR
problems at these frequencies.
Some contributions display more detailed spectral diagrams from which a reader may generally be able to discern the
attenuation at a particular frequency or the bandwidth of the null at a particular rejection ratio. The methods for
producing these plots are rarely described, or their desriptions are inconsistent. The number of samples used, and
the size and shape of windowing function may impact the diagram more than the technique under evaluation.
This contribution therefore proposes a uniform method for measuring DC suppression. Since the non-linear
distortion is expected to be worse closer to DC, and since the channel null is deeper at lower frequencies, it makes
sense to weight the function to place more value in energy at low frequencies. Since the noise from AC powerlines
is primarily at 50/60Hz and present to a lesser degree at 100/120 and 150/180, the measurement function should
include 50/60 and harmonics, but at an increasingly lower level. This contribution therefore proposes to evaluate
the DC suppression techniques by comparing the transmit power to the power of the transmit signal filtered by a
normalized Hamming window of length 64.1 That is, the measure of suppression should be calculated as follows:
N
p
n
Let pn be the transmitted sequence, where 1  n  N . Then
Orms 
n 1
N
2
is the rms. output level. The
 2 
k  ,0  k  63 . The output of convolving the
 63 
64-point hamming window is given as hk  0.54 0.46 cos
63
hamming window with
dn 
p
h
(n  m) m
m0
63
 hm
,1  n  N  63 . The rms. output at DC is given by
m0
1
The results presented here are independent of the specific choice of low-pass filter. Techniques which performed
better using this measurement criterion consistently yielded better attenuation at low frequencies.
2
N  63
d
n
ODC 
scale as
2
n 1
N  63
. And the measure of suppression is given by
AttenDC 
ODC
or given on a logarithmic
ORMS
ODC 
AttenDC  20 log 10
 dB . A plot of the fourier transform of a zero-padded 64-point hamming
 ORMS 
function is given in Figure 1.
Figure 1
3. 4kHz Suppression
Other contributions have proposed methods of suppressing the transmit spectrum at 4kHz. Some committee
members have indicated that suppression at 4kHz may not be necessary. If the committee deems 4kHz suppression
necessary, the same concept described in this contribution may be applied to evaluation of 4kHz suppression.
4. Symbol-Based Inversion
Other contributions have suggested to optionally invert the most significant bit, or sign bit, of one or more symbols
per frame. Several techniques have been proposed, including choosing the same symbol(s) every frame, choosing
the largest symbol(s) every frame, and choosing the optimal symbol(s) every frame. Some techniques suggested
choosing the inversion to drive the running digital sum (RDS) to zero, others suggested forcing a sign change in the
RDS whenever possible. While the matter is still disputed, recent contributions suggest that choosing optimal
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symbol(s) and zero-forcing the RDS are less optimal than the other approaches; therefore, these techniques are not
studied further in this contribution.
4.1 Choosing the same symbol(s) every frame
For purposes of analyzing the performance, choosing the two symbols per frame of frame size N is equivalent to
choosing one symbol per frame of frame size N/2. For this reason, when evaluating this technique we need only
look at how the amount of redundancy impacts the DC suppression.
At least two approaches are possible here; both involve choosing a smaller constellation for one symbol per frame.
The constellation could be reduced by limiting it to the positive half of the constellation space, and its sign bit would
be ignored by the receiver; or, the constellation could be reduced by “thinning” with a less significant bit describing
whether the sign should be inverted by the receiver. It is asserted without proof that the two yield identical
performance. The former provides decreased complexity.
For purposes of the simulation results which are displayed below, the constellation points are chosen at random from
the full constellation. On one symbol in every frame, the sign bit is inverted if it provides a symbol of opposite sign
from the RDS.
The algorithm may briefly be described as follows, operating a symbol at a time:
1.
Every N’th symbol, map using only the positive half of the constellation.
2.
If the RDS is positive, set the N’th symbol’s sign bit.
3.
Add the symbol to the RDS.
Figure 2 demonstrates the effectiveness of choosing the same symbol every frame as a function of frame size (or
redundancy). The “Baseline” in the chart represents the DC suppression achieved with out active means.2
2
All proposed constellations have a zero-mean. If using a mapping scheme which causes the probability of
selecting one constellation point as likely as selecting any other, a long sequences also has a zero-mean (and a null at
DC).
4
Symbol Based Inversion, fixed symbol location
0
DC suppression (dB)
-5
-10
-15
-20
-25
-30
-35
-40
-45
-50
8000
4000
2000
1000
500
250
redundancy (bps)
Baseline
8-point
253-point
Figure 2
As one might expect, symbol-based inversion with fixed symbol location offers better performance at higher
redundancy and smaller constellation size. At redundancy of 2kbps or less, symbol-based inversion offers marginal
(less than 6dB) performance.
Transmit PSD for fixed location (1:8)
0
PSD (dB)
-5
-10
-15
-20
-25
-30
0
4000
Frequency (Hz)
Figure 3
One undesirable side-effect of choosing a fixed-symbol location is that it creates peaks in the transmit power
spectrum (see Figure 3). These peaks occur at fractions related to the frame size. That is, when the sign bit of
every other symbol is adjusted (1 out of 2), there is a peak in the spectrum at 2*pi/2 or 4kHz. If every fourth
symbol is adjusted, there are peaks at pi/2 and pi or 2kHz and 4kHz.
5
4.2 Choosing the largest symbol(s) in each frame
Unlike choosing symbols at fixed locations, it is not immediately apparent that choosing the largest symbol from a
frame of size N and the two largest symbols from a frame of size 2N is equivalent. Simulation results (see Figure 4)
reveal that they perform comparably.
Symbol Based Inversion, largest symbol(s)
0
-5
DC Suppression (dB)
-10
-15
-20
-25
-30
-35
-40
-45
-50
8000
4000
Baseline
2000
1000
500
250
Redundancy (bps)
Largest symbol
2 Largest symbols
Figure 4
A simple symbol-based algorithm using the largest symbol in each frame is as follows:
1.
Map the entire frame. For a fixed (perhaps the first, perhaps the last) symbol location, use a reduced
constellation with a less significant bit (perhaps the second from least significant bit) forced to zero.
2.
Compute the RDS including all symbols from the frame except the largest. If there are two symbols of
equal magnitude, choose the first.
3.
Set the sign bit of the largest symbol to represent opposite sign from the RDS. If the symbol was inverted
in the process, set the sign inversion bit in the symbol with the reduced constellation.
4.
Add the new, largest symbol to the RDS.
Figure 5 compares the performance of two symbol-based inversion schemes: fixed location and largest symbol. An
8-point constellation was used for both measurements. At one bit per symbol (8kbps redundancy), the two methods
are the same. At lower levels of redundancy, choosing the largest symbol provides better DC suppression than a
fixed location. Choosing the largest symbol has a further advantage in that it does not cause peaks in the transmit
spectrum.
6
Symbol baed Inversion,
comparison of fixed to largest symbol
0
DC suppression (dB)
-5
-10
-15
-20
-25
-30
-35
-40
-45
-50
8000
4000
2000
1000
500
250
redundancy (bps)
Baseline
Fixed locatoin
Largest symbol
Figure 5
5. Frame-Based Inversion
Other contributions have proposed two techniques for suppressing low frequency transmit energy by performing
frame-based inversion. The simplest and most efficient of the techniques suggests optionally inverting the sign bits
of every symbol in the frame to cause the frame’s digital sum to have the opposite sign from the RDS. Another
contribution has suggested extending the frame size, dividing the frame into two subframes, and optionally inverting
the sign bits separately for each sub-frame. This technique allows a balance between DC suppression and 4kHz
suppression.
5.1 Inverting the entire frame
The simplest technique is to determine at the start of the frame whether the sign bits for the entire frame should be
inverted. An algorithm for performing the frame inversion follows:
1.
Map the entire frame. For the first symbol in the frame, use only the positive half-constellation.
2.
Compute the forward RDS, that is the sum of values in the new frame only.
3.
If the RDS and forward RDS are of the same sign, invert every symbol in the frame.
4.
Add the new frame to the RDS.
Figure 6 shows the results of using this technique with different constellation sizes. Variable redundancy was
achieved by varying the frame size. As in symbol-based inversion, the larger constellation provided poorer DC
suppression.
7
Frame Based Inversion
0
-5
DC Suppression (dB)
-10
-15
-20
-25
-30
-35
-40
-45
-50
8000
4000
2000
1000
500
250
redundancy (bps)
Baseline (8pt)
8-point
253-point
Figure 6
5.2 Dividing the frame into sub-frames
An extension of the frame inversion technique is to divide the frame into interleaved sub-frames. The sub-frames
can be optionally inverted to encourage a sign change of the RDS. As demonstrated in Figure 7, this results in a
reduction in effectiveness of DC suppression.
The following algorithm would produce interleave frame-based inversion:
1.
Map the entire frame. For the first n symbols (where n is the number of sub-frames), use only the positive
half-constellation.
2.
For each sub-frame, compute the forward RDS of each sub-frame by computing the sum of the interleaved
sub-frame. If the RDS and forward RDS are of the same sign, invert the sub-frame.
3.
Add the new forward RDS to the RDS.
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Interleaved Frame Based Inversion
0.00
DC Suppression (dB)
-5.00
-10.00
-15.00
-20.00
-25.00
-30.00
-35.00
-40.00
-45.00
-50.00
8000
4000
2000
1000
500
250
Redundancy (bps)
One sub-frame
Odd/even
4:1 interleave
8:1 interleave
Figure 7
6. Comparing Symbol and Frame-Based Inversion Techniques
Among symbol-based inversion techniques evaluated, the best performer was the inversion of the largest symbol in
each frame. Among the frame-based inversion techniques, using a single sub-frame achieved the highest
performance. Based on Figure 8 and Figure 9, frame-based inversion techniques yield better DC suppression than
symbol-based inversion techniques over different constellation sizes and different levels of redundancy.
Symbol and Frame Based Inversion
8-point Constellation
0.00
DC Suppression (dB)
-5.00
-10.00
-15.00
-20.00
-25.00
-30.00
-35.00
-40.00
-45.00
-50.00
8000
4000
2000
1000
500
Redundancy (bps)
Baseline
Symbol Based
Figure 8
9
Frame Based
250
Symbol and Frame Based Inversion
253-point constellation
0.00
DC suppression (dB)
-5.00
-10.00
-15.00
-20.00
-25.00
-30.00
-35.00
-40.00
8000
4000
2000
1000
500
250
redundancy (bps)
Baseline
Symbol Based
Frame Based
Figure 9
7. Recommendations
Based on simulations, the results of which are presented above, this contribution recommends the selection of
frame-based sign inversion to accomplish DC suppression.
Further analysis of frame-based inversion reveals that significant DC suppression can be accomplished with
redundancy of 250bps or less. Since variable transmit spectrum shaping offers performance advantages, this
contribution further recommends the support of low redundancy frame-based inversion. This could be
accomplished through three means which are only marginally different.
Method 1 provides for variable frame size. After probing, the receiver would select the frame sizes from a wide
range (perhaps 1 to roughly 64 symbols - this could be limited by the transmitter). An algorithm such as one
suggested in Section 5.1 could be used. This appears the simples and most attractive method.
Method 2 provides for large frame - about 64 symbols. As a result of probing, the receiver would select that
between one and 64 sign inversion bits be used to invert non-interleaved sub-frames. The frame would be evenly
divided into sub-frames, each of which would require one sign inversion bit carried in the next frame.
Method 3 provides for a small frame - 6 or 8 symbols. The receiver would indicate after probing how many sign
inversion bits per frame should be used, and, if one, to how many frames that bit should apply. If more than one
sign inversion bit is used per frame, the frame would be divided into sub-frames with a separate sign inversion bit
applying to each.
If the committee decides 4kHz suppression is necessary, an interleaved frame inversion technique could apply.
Conversely, if the committee decides that 4kHz suppression is unnecessary, this contribution recommends the use
of non-interleaved frame-based sign inversion.
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8. References
[1] RSA Communication: “DC Suppresser for 56K Modems” Raleigh. October 1996.
[2] Rockwell: “Proposed PCM Modem Transmitted Signal Spectrum” Irvine. November 1996.
[3] RSA Communication: “DC Suppresser for 56K Modems” Irvine. November 1996.
[4] Motorola: “A Spectral Shaping Technique for PCM Modems” Irvine. November 1996.
[5] Rockwell: “Spectral Shaping with Variable Redundancy” Orlando. December 1996.
[6] ESS Technology: “Using Frame Inversion for DC Suppression in PCM modems” Fort Lauderdale. January
1997.
[7] RSA Communication: “Frame Inversion for Spectrum Shaping with Sign Inversion Bit in the Current Frame”
For Lauderdale. January 1997.
[8] U.S. Robotics: “Frame Oriented Spectral Shaping Technique” Fort Lauderdale. January 1997.
[8] RSA Communication: “Performance Simulation of Transmit Spectrum Shapling” Irvine. March 1997.
[9] VoCAL Technologies: “Variable Transmit Spectral Shaping” Irvine. March 1997[
[10] Intel: “Candidate Downstream Signal Constellations” Irvine. March 1997.
[11] ESS Technology: “Why frame based inversion” Irvine. March 1997.
[12] ESS Technology: “New Algorithms Using Two Sign Inversion Bits for PCM Spectral Shaping” Irvine.
March 1997.
With special thanks to Ofir Shalvi
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